Use your LLC's name and Employer Identification Number (EIN). The fewer people who have your Social Security number, the better.
Don't worry if you have a "disregarded entity" (i.e. a single member LLC), because your 1099's will come in the name of your LLC. When you fill out your Self-employed tax return, you will have an opportunity to report your business name and EIN to the IRS, so that your income can be matched properly.
